A Comparison Between Three Variable-Step Algorithms for the Integration of the Equations of Motion in Structural Dynamics

Three variable-step algorithms for time integrating the equations of motion in structural and mechanism analysis are compared. The analysed algorithms are: the Thomas and Gladwell scheme (1,2), which we modified in reference (3) for application to systems of differential/algebraic equations (VSA23); the Hilber, Hughes and Taylor scheme (HNT) (4,5) with a step-size control strategy; and the DASSL code, developed by L. Petrold (6) and distributed through the NETLIB computer library network. A short theory about the error estimation techniques used by the VSA23 and HNT algorithms is presented. Some numerical test examples are shown, representing the kind of problems the user is faced to in practical applications.